Robust Event-Triggered Control Invariance of Probabilistic Boolean Control Networks

In this brief, the robust control invariance problem of probabilistic Boolean control networks (PBCNs) is investigated by a class of event-triggered control (ETC), which is an intermittent control scheme in essential. By resorting to the semi-tensor product (STP) technique, a PBCN with ETC can be equivalently described in a form of an algebraic linear system. Based on which, a matrix testing condition is derived to judge whether the given set can be a robust ETC invariant set (RETCIS). Subsequently, a necessary and sufficient condition is developed for the existence of event-triggered controllers. Meanwhile, all feasible event-triggered controllers are designed for guaranteeing the given set to be an RETCIS. Finally, a biological example is employed to demonstrate the availability of theoretical results.